[87.07] The Cosmological Mass Distribution Function in the Zel'dovich Approximation

J. Lee, S. F. Shandarin (U. Kansas)

An analytic estimation of the mass function for gravitationally bound
objects is presented. We use the Zel'dovich approximation
to extend the Press-Schecter formalism to a nonspherical
dynamical model. In the Zel'dovich approximation,
the gravitational collapse along all three directions
which will eventually lead to the formation of real virialized
objects - clumps occur in the regions where the lowest eigenvalue
of the deformation tensor, \lambda_3 is positive.
We derive the conditional probability of \lambda_3 > 0
as a function of the linearly extrapolated density contrast
\delta, and the conditional probability distribution of \delta
provided that \lambda_3>0.
These two conditional probability distributions show that
the most probable density of the bound regions (\lambda_3>0)
is roughly 1.5 at the characteristic mass scale M_*,
and that the probability of \lambda_3 > 0 is almost unity
in the highly overdense regions (\delta > 3\sigma).
Finally the analytic mass function of clumps is derived with a help
of one simple ansatz which is employed to approach the multistream
regimes beyond the validity of the Zel'dovich approximation.
The resulting mass function is renormalized by a factor
of 12.5, which we justify with a sharp k-space filter
by means of the modified Jedamzik analysis.
Our mass function is shown to be different from the
Press-Schecter one, having a lower peak and predicting more
small-mass objects.